I got my hands on a 1972 80 gallon 2 stage compressor. The pump is a Quincy
model 325 13. I understand that this is the compressor on their QR series
machines. It is in great shape, has a 5 HP Single Phase Motor and a
magnetic starter. All the wiring has been removed.

Here are some questions I hope you can help me with:

What order does the unit get wired in? Is it line voltage to - pressure
switch to magnetic starter to motor?

What kind of oil should I use?

It is missing the air filter assembly, where can I purchase a new one?

It should use a regular 1" air filter, available at Grainger or any
air compressor repair outfit. Try your Yellow Pages.

On my Quincy I had to replace the belts -- it took a matched pair of B47s
or something -- and I went to Grainger and asked for a matched pair and
they told me they are all matched nowadays. One belt was however slightly
longer than the other. I figure the short one will soon stretch out. But
if I had to do it over I'd look up "power transmission" in the Yellow
Pages and call every place looking for a deal. Those damn belts cost waaay
too much at Grainger. Then I'd go to their will call and make the clerk
bring me ALL of the belts in that size and hand pick the two closest in
length. If you're going to spend $40 on 2 belts, you should get to pick. - GWE

The compressor is hopelessly broken, I can relieve you from it for
$20. :) Just kidding.

Have you tried the obvious, calling Quincy and checking out their
website. They may be able to send/sell you some manuals and may give
good advice. I recall buying a used dental compressor, which was
leaking air. I called the manufacturer, they gave me some good
suggestions, I was able to download manuals etc. The problem was a
tiny hose leading to a pressure switch, that simply fell off. Simple
messing around with a screwdriver and thinking logically did it.

Also, you can talk to the motor manufacturer. Open up the pressure
switch box, the motor wiring box, and see what you can find. See if
there is a relay of some kind somewhere.

Your task is not that complicated. A few hours of working and a few
more hours of thinking should do it. Would be nice to make sure that
you have a on/off switch right on the compressor, when you are done.